First, divide the original measurements with the scaled ones. You'll get the same answer meaning that is the scale used by the model.
1500 ft. ÷7.5 ft = 200
600 ft. ÷ 3 ft. = 200
To simply check, if you divide 1500 with 200, the answer is 7.5 and 600 divided by 200 is 3.
To find the scaled dimension of the tennis court with actual dimension of 120 ft by 60 ft, divide both values with the scale used in the model which is 200.
120 ft. ÷ 200 = 0.6 ft
60 ft. ÷ 200 = 0.3 ft
The dimension of the tennis court in the scaled model is 0.6 ft long and 0.3 ft. wide.
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
Clod would get 11, because the number they both thought of was 63
So what I did was as $32.50 twice and got $65.00 and subtracted it with $212.50 and got $152.50. Hope i was helpful!
